Tom will need to offer additional collateral of C. $2,437.50 to borrow enough for his planned vacation.
Collateral refers to a valued property or financial security offered by the borrower to the lender to guarantee repayment of a loan.
Lenders sell collaterals when the borrowers fail to comply with their loan terms.
Car's value = $3,500
Collateral value in percentage = 80%
Car's collateral value = $2,800 ($3,500 x 80%)
Planned cost of vacation = $4,750
Additional cost to meet vacation cost = $1,950 ($4,750 - $2,800)
Additional collateral value to meet target = $2,437.50 ($1,950/80%)
Total collateral that Tom needs to offer = $5,937.50 ($3,500 + $2,437.50)
80% of $5,937.50 = $4,750
Another way is to work with the planned cost and the collateral percentage offered by Tom's bank:
Planned cost of vacation = $4,750
Collateral value in percentage = 80%
Total collateral to be offered by Tom = $5,937.50 ($4,750/80%)
Car's collateral value = $3,500
Additional collateral value = $2,437.50 ($5,937.50 - $3,500)
Thus, Tom needs additional collateral of C. $2,437.50.
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Answer:
Knowing that those vectors start at the point (0,0) we can "think" them as lines.
As you may know, two lines are parallel if the slope is the same, then we can find the "slope" of the vectors and see if it is the same.
A) the vectors are: (√3, 1) and (-√3, -1)
You may remember that the way to find the slope of a line that passes through the points (x1, y1) and (x2, y2) is s = (y2 - y1)/(x2 - x1)
Because we know that our vectors also pass through the point (0,0)
then the slopes are:
(√3, 1) -----> s = (1/√3)
(-√3, -1)----> s = (-1/-√3) = (1/√3)
The slope is the same, so the vectors are parallel.
Part B:
The vectors are: (2, 3) and (-3, -2)
the slopes are:
(2, 3) -----> s = 3/2
(-3, -2)----> s = -2/-3 = 2/3
the slopes are different, so the vectors are not parallel.
∥v∥=√((6)^2+(-8)^2)=√(36+64)=√100=10. Dividing v by its magnitude, we get the unit vector u=(v/∥v∥)=(6i−8j)/10=(3/5)i−(4/5)j. Therefore, two unit vectors parallel to v are (3/5)i−(4/5)j and −(3/5)i+(4/5)j.
a. Two unit vectors parallel to v=6i−8j can be found by dividing the vector v by its magnitude. The magnitude of v can be calculated using the formula ∥v∥=√(v1^2+v2^2), where v1 and v2 are the components of v in the x and y directions, respectively. In this case, v1=6 and v2=−8. Thus,
b. To find the value of b when v=⟨1/3,b⟩ is a unit vector, we need to calculate the magnitude of v and set it equal to 1. The magnitude of v is given by ∥v∥=√((1/3)^2+b^2). Setting this equal to 1, we have √((1/3)^2+b^2)=1. Squaring both sides of the equation, we get (1/3)^2+b^2=1. Simplifying, we have 1/9+b^2=1. Rearranging the equation, we find b^2=8/9. Taking the square root of both sides, we get b=±(2√2)/3. Therefore, the value of b when v is a unit vector is b=(2√2)/3 or b=−(2√2)/3.
c. To find all values of a such that w=ai−a/3j is a unit vector, we need to calculate the magnitude of w and set it equal to 1. The magnitude of w is given by ∥w∥=√(a^2+(-a/3)^2). Setting this equal to 1, we have √(a^2+(-a/3)^2)=1. Simplifying, we get a^2+(a^2/9)=1. Combining like terms, we have (10/9)a^2=1. Dividing both sides by 10/9, we get a^2=(9/10). Taking the square root of both sides, we have a=±√(9/10). Therefore, the values of a such that w is a unit vector are a=√(9/10) or a=−√(9/10).
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There are
the seats are chosen
ways that 4 seats can be left empty in the auditorium. This is a
important.
Answer:
5773185
Step-by-step explanation:
There are 110 seats
110 ways to choose the first empty seat
Now there are 109 seats
109 ways to choose the next empty seat
Now there are 108 seats
108 ways to choose the next empty seat
Now there are 107 seats
110*109*108*107=138556440
Now the order of the empty seats doesn't matter so we need to divide by 4!
138556440/ 4!
138556440/ 24
5773185
In this mathematics problem, we are asked to determine the number of ways that 4 seats can be left empty in a high school auditorium that seats 110 people. We can use the concept of combinations to solve this.
In this problem, we are asked to determine the number of ways that 4 seats can be left empty in a high school auditorium that seats 110 people. To solve this, we can use the concept of combinations. The total number of ways to choose 4 seats out of 110 is represented by the combination formula: C(110, 4). To calculate this, we can use the formula: C(n, r) = n! / (r!(n - r)!), where n is the total number of seats and r is the number of seats left empty. Plugging in the values, we have C(110, 4) = 110! / (4!(110 - 4)!).
Using a calculator, we can simplify this expression and calculate the answer.
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patient records, but that source doesn't allow us to compare people who use health services with those who don't. Therefore, the US Department of Health and Human Services conducted the
Florida Health Survey, which was used to interview a random sample of 62,348 people who live in the state of Florida.
Part A: What is the population for this sample survey? What is the sample? (4 points)
Part B: The survey found that 74% of males and 83% of females in the sample had visited a general practitioner at least once during the past year. Do you think these estimates are close to
the truth about the entire population? Explain. (6 points) (10 points)
Answer:
A)i) Population: Total number of people that reside in Florida..
II) Sample: 62348 people that took part in the random survey.
B) No, the estimates are not close to the truth of the entire population.
Step-by-step explanation:
A)i) The population is the total number of people that reside in Florida.
II) The sample is the 62348 people that took part in the random survey.
B) From the details given in the question, we will see that people who are not part of the healthcare system weren't included due to the fact that they used patients records to judge. This means that if they don't have healthcare, then they will have no patient records. Therefore, we can conclude that the estimates are not close to the truth of the entire population due to the fact that that those who weren't part of the Healthcare system were not considered.
if you don’t know answer don’t even comment
Answer:
y = 1/4 x - 1 (y = 0.25 x - 1)
Step-by-step explanation:
x intercept: (4 , 0)
y intercept: (0 , -1)
rise: 1
run: 4
slope: rise/run = 1/4
equation: y = mx + b m=1/4 b = -1
y = 1/4 x - 1
Answer:
boys = 272
Step-by-step explanation:
b = boys
g = girls
1) write two equations with the given informations:
g + b = 650
g = b + 106
2) substitute the value of g in the first equation:
b + 106 + b = 650
3) solve the equation for b
2b = 544
b = 272
4) substitute the value in the second equation
g = 272 + 106
g = 378
girls = 378
boys = 272
Answer:
1/3
Step-by-step explanation: